Calderdale and Huddersfield NHS Foundation Trust is expected to be £25m in deficit by the end of the year.

A reorganisation of the hospitals to make sure patients get safe treatment could see Huddersfield and Halifax served by a single A&E, along with urgent care centres treating patients with less serious conditions.

Ms Lynch said: “During the general election campaign, the Prime Minister came to my constituency and promised to keep Calderdale Royal’s A&E department open and sort out the financial mess that our hospital was in.

“Since then, the government have back-tracked on both promises, saying that these are matters for the local NHS trust and for the clinical commissioning group.

“Will the Prime Minister show that he is a man of his word by meeting me to discuss ways in which he can honour his election promises?”

Mr Cameron responded by saying the government was investing £10bn in the NHS.

He said: “We certainly haven’t back tracked on what we promised.

“We said we would put more money into the NHS. Calderdale Hospital is an absolutely vital service.”

NHS services in Calderdale and Huddersfield face a £155m funding shortfall by 2021.

Nationally, fears have been raised that the government’s £10bn investment will fall way short of a £30bn funding gap the whole health service faces in the same period.

Ms Lynch added: “Figures released this week show the NHS is now in the grips of the worst financial crisis in a generation, and our NHS Foundation Trust here in Calderdale desperately needs government help with its crippling debts.”

A public consultation over the future of hospital services in Calderdale and Huddersfield has been delayed until next year.